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Abstract:
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Group testing has been widely used to reduce the cost of large-scale screening individuals for rare diseases. Motivated by the recent development of multiplex assays, screening procedures now involve detecting individuals in pools for multiple infections simultaneously. Previous models for multiple-infection group testing data are restricted to making potentially unrealistic assumptions (e.g., logistic link function) and/or they ignore individual covariate information. To overcome these limitations, we propose a copula-assisted single-index regression model for modeling multiple group testing data. For each disease, a single-index model is fit, while, crucially, the single-index itself is common to all diseases, and the nonparametrically estimated functions of the single-index are approximated by distinct I-splines estimators. The copula method is adopted to jointly use the multiple-infection group testing data simultaneously rather than one disease at a time. Moreover, we develop a generalized Expectation-Maximization algorithm to solve the problem and establish asymptotic results. Finally, we illustrate our methods via simulation and a real application.
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